Jian Feng HUANG; Yuan Heng WANG
Suppose E is a Banach space with uniformly normal structure and suppose E also has uniformly Gateaux differentiable norm.Let A be an m-accretive operator such that C = D(A) is a convex subset of E.Let {α_n} be a sequence in the interval (0,1) and let {r_n} be a sequence in the interval (0,∞).Then,under some suitable conditions,the sequence {x_n} defined by (1.2) converges strongly to an element of A~(-1)(0).Secondly,we also prove that:Let E be a uniformly convex Banach space whose norm is Frechet differentiable.Let {α_n},{β_n} be two squences in the interval (0,1) and let {r_n} be a sequence in the interval (0,∞).If A~(-1) (0)∩B~(-1)(0)≠0,then,under some suitable conditions,the sequence {x_n} defined by (3.20) converges weakly to an element in A~(-1)(0)∩B~(-1)(0).Our results extend and improve Theorem 2 of Kamimura, Takahashi (2000) and theorem 4.1,Theorem 4.2,Theorem 4.3 of Xu (2006):(i) In Theorem 2 of Kamimura,Takahashi (2000),the condition"Every bounded,closed and convex subset of a reflexive Banach space has the fixed point property for nonexpansive mappings"is removed;(ii) In Xu H.K.(2006),the condition"E is reflexive and has a weakly continuous duality map J_■"is replaced by"E is a Banach space with uniformly normal structure and E also has uniformly Gateaux differentiable norm."so that it contains some Banach spaces besides the Banach space which is in Xu H.K.(2006). At the same time,we state how to approximate a common zero of two m-accretive operators in E.Hence,the results also improve and unify some corresponding results.